A Wake Model for Free-Streamline Flow Theory Part I. Fully and Partially Developed Wake Flows and Cavity Flows past an Oblique Flat Plate

Abstract

A wake model for the free-streamline theory is proposed to treat the two-dimensional flow past an obstacle with a wake or cavity formation. In this model the wake flow is approximately described in the large by an equivalent potential flow such that along the wake boundary the pressure first assumes a prescribed constant under-pressure in a region downstream of the separation points (called the near-wake) and then increases continuously from this under-pressure to the given free stream value in an infinite wake strip of finite width (the far-wake). The boundary of the wake trailing a lifting body is allowed to change its slope and curvature at finite distances from the body and is required to be parallel to the main stream only asymptotically at downstream infinity. The pressure variation along the far-wake takes place in such a way that the upper and lower boundaries of the far-wake form a branch slit of undetermined shape in the hodograph plane. One advantage of this wake model is that it provides a rather smooth continuous transition of the hydrodynamic forces from the fully developed wake flow to the fully wetted flow as the wake disappears. When applied to the wake flow past an inclined flat plate, this model yields the exact solution in a closed form for the whole range of the wake under-pressure coefficient. The separated flow over a slightly cambered plate can be calculated by a perturbation theory based on this exact solution.

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